pbpt::math Namespace Reference

The namespace for math library implementation. More...

Namespaces
namespace	detail
	Contains internal implementation details for the math library.

Classes
class	BoundingBox
class	Homogeneous
	A template class for an N-dimensional homogeneous coordinate. More...
class	Matrix
	A template class for RxC dimensional mathematical matrices. More...
class	MatrixView
	A non-owning, mutable view/proxy into a sub-region of another Matrix. More...
class	Normal
class	Point
	A template class for an N-dimensional point in space. More...
class	Ray
	A template class for an N-dimensional geometric ray. More...
class	RayDifferential
class	Transform
	A namespace for 3D transformation factory functions. More...
class	Vector
	A template class for N-dimensional mathematical vectors. More...
class	VectorView
	A non-owning, mutable view/proxy of vector-like data. More...

Typedefs
using	Bound3 = BoundingBox<Float, 3>
	3D bounding box
using	Bound2 = BoundingBox<Float, 2>
	2D bounding box
using	Float = float
	The primary floating-point type used throughout the math library.
using	Homo3 = Homogeneous<Float, 3>
	A 3-dimensional homogeneous coordinate using the library's default Float type.
using	Homo2 = Homogeneous<Float, 2>
using	Mat2 = Matrix<Float, 2, 2>
	A 2x2 matrix of type Float.
using	Mat3 = Matrix<Float, 3, 3>
	A 3x3 matrix of type Float.
using	Mat4 = Matrix<Float, 4, 4>
	A 4x4 matrix of type Float.
using	Mat3x4 = Matrix<Float, 3, 4>
	A 3x4 matrix of type Float.
using	Mat4x3 = Matrix<Float, 4, 3>
	A 4x3 matrix of type Float.
using	Pt2 = Point<Float, 2>
	A 2-dimensional point of type Float.
using	Pt3 = Point<Float, 3>
	A 3-dimensional point of type Float.
using	Pt4 = Point<Float, 4>
	A 4-dimensional point of type Float.
using	Ray3 = Ray<Float, 3>
	A 3-dimensional ray of type Float, commonly used in 3D graphics.
using	Ray2 = Ray<Float, 2>
	A 2-dimensional ray of type Float.
using	RayDiff3 = RayDifferential<Float, 3>
using	Vec2 = Vector<Float, 2>
	A 2-dimensional vector of type Float.
using	Vec3 = Vector<Float, 3>
	A 3-dimensional vector of type Float.
using	Vec4 = Vector<Float, 4>
	A 4-dimensional vector of type Float.
using	Normal2 = Normal<Float, 2>
	A 2-dimensional vector of type Float.
using	Normal3 = Normal<Float, 3>
	A 3-dimensional vector of type Float.
using	Normal4 = Normal<Float, 4>
	A 4-dimensional vector of type Float.

Functions
template<typename T>
constexpr T	abs (T x)
	A constexpr implementation of the absolute value function.
template<typename T> requires std::is_floating_point_v<T>
constexpr T	rad2deg (T rad)
	Converts an angle from radians to degrees.
template<typename T> requires std::is_floating_point_v<T>
constexpr T	deg2rad (T deg)
	Converts an angle from degrees to radians.
template<typename T>
constexpr T	sqrt (T x)
	Calculates the square root of a number with constexpr support.
template<typename T> requires std::is_floating_point_v<T>
constexpr T	sin (T x)
	Calculates the sine of an angle with constexpr support.
template<typename T> requires std::is_floating_point_v<T>
constexpr T	cos (T x)
	Calculates the cosine of an angle with constexpr support.
template<typename T> requires std::is_floating_point_v<T>
constexpr T	tan (T x)
	Calculates the tangent of an angle with constexpr support.
template<typename T> requires std::is_floating_point_v<T>
constexpr bool	is_equal (T a, T b)
	Compares two floating-point values for equality.
template<typename T> requires std::is_floating_point_v<T>
constexpr bool	is_greater (T a, T b)
	Compares if a is greater than b.
template<typename T> requires std::is_floating_point_v<T>
constexpr bool	is_less_equal (T a, T b)
	Compares if a is less than or equal to b.
template<typename T> requires std::is_floating_point_v<T>
constexpr bool	is_less (T a, T b)
	Compares if a is less than b.
template<typename T> requires std::is_floating_point_v<T>
constexpr bool	is_greater_equal (T a, T b)
	Compares if a is greater than or equal to b.
template<typename T, int N>
constexpr std::vector< Vector< T, N > >	get_orthogonal_bases (const Vector< T, N > &base)
	Returns orthogonal bases for a given vector.
template<typename T>
constexpr std::vector< Vector< T, 2 > >	get_orthogonal_bases (const Vector< T, 2 > &base)
	Returns orthogonal bases for a given vector when N == 2.
template<typename T>
constexpr std::vector< Vector< T, 3 > >	get_orthogonal_bases (const Vector< T, 3 > &base)
	Returns orthogonal bases for a given vector when N == 3.

Detailed Description

The namespace for math library implementation.

Typedef Documentation

Float

using pbpt::math::Float = float

The primary floating-point type used throughout the math library.

This type alias controls the precision of geometric and mathematical calculations.

• If the FLOAT_64BIT preprocessor macro is defined, Float will be a double (64-bit).
• Otherwise, Float will default to a float (32-bit).

Note

To use double-precision floating-point numbers, define the FLOAT_64BIT macro in your project's build settings, for example, by passing the -DFLOAT_64BIT flag to your C++ compiler.

Function Documentation

abs()

template<typename T>

T pbpt::math::abs ( T x )

constexpr

A constexpr implementation of the absolute value function.

Template Parameters

T	The arithmetic type of the number.

Parameters

x	The number to get the absolute value of.

Returns

The absolute value of x.

cos()

template<typename T>
requires std::is_floating_point_v<T>

T pbpt::math::cos ( T x )

constexpr

Calculates the cosine of an angle with constexpr support.

At compile-time, uses a Taylor series. At runtime, calls std::cos. It can be implemented efficiently by shifting the angle and calling pbpt::math::sin.

Template Parameters

T	Floating-point type of the angle.

Parameters

x	The angle in radians.

Returns

The cosine of x.

deg2rad()

template<typename T>
requires std::is_floating_point_v<T>

T pbpt::math::deg2rad ( T deg )

constexpr

Converts an angle from degrees to radians.

Template Parameters

T	The floating-point type of the angle.

Parameters

deg	The angle in degrees.

Returns

The angle in radians.

get_orthogonal_bases() [1/3]

template<typename T>

std::vector< Vector< T, 2 > > pbpt::math::get_orthogonal_bases ( const Vector< T, 2 > & base )

inlineconstexpr

Returns orthogonal bases for a given vector when N == 2.

Template Parameters

Args	The types of the orthogonal vectors.

Parameters

u	The input vector.

Returns

A vector of orthogonal vectors.

get_orthogonal_bases() [2/3]

template<typename T>

std::vector< Vector< T, 3 > > pbpt::math::get_orthogonal_bases ( const Vector< T, 3 > & base )

inlineconstexpr

Returns orthogonal bases for a given vector when N == 3.

Template Parameters

Args	The types of the orthogonal vectors.

Parameters

base	The input vector.

Returns

A vector of orthogonal vectors.

get_orthogonal_bases() [3/3]

template<typename T, int N>

std::vector< Vector< T, N > > pbpt::math::get_orthogonal_bases ( const Vector< T, N > & base )

inlineconstexpr

Returns orthogonal bases for a given vector.

Template Parameters

Args	The types of the orthogonal vectors.

Parameters

base	The input vector.

Returns

A vector of orthogonal vectors.

is_equal()

template<typename T>
requires std::is_floating_point_v<T>

bool pbpt::math::is_equal ( T a, T b )

constexpr

Compares two floating-point values for equality.

This function checks if the absolute difference between a and b is less than a predefined epsilon (EPSILON). This is a conservative approach, but it's useful in constexpr contexts where exact comparisons are not always possible.

Template Parameters

T	Floating-point type of the values.

Parameters

a	The first value.
b	The second value.

Returns

true if abs(a - b) < EPSILON, false otherwise.

is_greater()

template<typename T>
requires std::is_floating_point_v<T>

bool pbpt::math::is_greater ( T a, T b )

constexpr

Compares if a is greater than b.

This function checks if a - b is greater than a predefined epsilon (EPSILON).

Template Parameters

T	Floating-point type of the values.

Parameters

a	The first value.
b	The second value.

Returns

true if a - b > EPSILON, false otherwise.

is_greater_equal()

template<typename T>
requires std::is_floating_point_v<T>

bool pbpt::math::is_greater_equal ( T a, T b )

constexpr

Compares if a is greater than or equal to b.

This function checks if a - b is greater than a predefined epsilon (EPSILON).

Template Parameters

T	Floating-point type of the values.

Parameters

a	The first value.
b	The second value.

Returns

true if a - b > EPSILON, false otherwise.

is_less()

template<typename T>
requires std::is_floating_point_v<T>

bool pbpt::math::is_less ( T a, T b )

constexpr

Compares if a is less than b.

This function checks if b - a is greater than a predefined epsilon (EPSILON).

Template Parameters

T	Floating-point type of the values.

Parameters

a	The first value.
b	The second value.

Returns

true if b - a > EPSILON, false otherwise.

is_less_equal()

template<typename T>
requires std::is_floating_point_v<T>

bool pbpt::math::is_less_equal ( T a, T b )

constexpr

Compares if a is less than or equal to b.

This function checks if b - a is greater than a predefined epsilon (EPSILON).

Template Parameters

T	Floating-point type of the values.

Parameters

a	The first value.
b	The second value.

Returns

true if b - a > EPSILON, false otherwise.

rad2deg()

template<typename T>
requires std::is_floating_point_v<T>

T pbpt::math::rad2deg ( T rad )

constexpr

Converts an angle from radians to degrees.

This function converts an angle from radians to degrees.

Template Parameters

T	The floating-point type of the angle.

Parameters

rad	The angle in radians.

Returns

requires constexpr

sin()

template<typename T>
requires std::is_floating_point_v<T>

T pbpt::math::sin ( T x )

constexpr

Calculates the sine of an angle with constexpr support.

At compile-time, uses a Taylor series. At runtime, calls std::sin. The compile-time version performs range reduction to maintain precision.

Template Parameters

T	Floating-point type of the angle.

Parameters

x	The angle in radians.

Returns

The sine of x.

sqrt()

template<typename T>

T pbpt::math::sqrt ( T x )

constexpr

Calculates the square root of a number with constexpr support.

This function intelligently switches its implementation based on the evaluation context.

• At compile-time (inside a constexpr expression), it uses a constexpr-friendly Newton-Raphson implementation (detail::sqrt_newton_raphson).
• At runtime, it calls the standard library's std::sqrt, which is typically faster and more accurate due to hardware-specific optimizations (e.g., FPU instructions).

This dual approach provides both compile-time evaluation capabilities and runtime performance.

Template Parameters

T	The arithmetic type of the number.

Parameters

x	The non-negative number to find the square root of.

Returns

The square root of x.

Exceptions

std::runtime_error

If a negative x is passed at runtime.

Note

Providing a negative x at compile-time will result in a compilation error.

tan()

template<typename T>
requires std::is_floating_point_v<T>

T pbpt::math::tan ( T x )

constexpr

Calculates the tangent of an angle with constexpr support.

This function is implemented as sin(x) / cos(x), automatically leveraging their context-aware constexpr behavior.

Template Parameters

T	Floating-point type of the angle.

Parameters

x	The angle in radians.

Returns

The tangent of x.